Tracing shock type with chemical diagnostics

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https://doi.org/10.1051/0004-6361/201936536 c

ESO 2020

Astronomy

&

Astrophysics

Tracing shock type with chemical diagnostics

An application to L1157

T. A. James¹, S. Viti¹, J. Holdship¹, and I. Jiménez-Serra²

1 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK e-mail: [email protected]; [email protected]

2 Centro de Astrobiologia (CSIC, INTA), Ctra. de Ajalvir, km. 4, Torrejón de Ardoz 28850, Madrid, Spain Received 20 August 2019/ Accepted 4 December 2019

ABSTRACT

Aims.The physical structure of a shock wave may take a form unique to its shock type, implying that the chemistry of each shock type is unique as well. We aim to investigate the different chemistries of J-type and C-type shocks in order to identify unique molecular tracers of both shock types. We apply these diagnostics to the protostellar outflow L1157 to establish whether the B2 clump could host shocks exhibiting type-specific behaviour. Of particular interest is the L1157-B2 clump, which has been shown to exhibit bright emission in S-bearing species and HNCO.

Methods.We simulate, using a parameterised approach, a planar, steady-state J-type shock wave using UCLCHEM. We compute a grid of models using both C-type and J-type shock models to determine the chemical abundance of shock-tracing species as a function of distance through the shock and apply it to the L1157 outflow. We focus on known shock-tracing molecules such as H2O, HCN, and CH3OH.

Results.We find that a range of molecules including H2O and HCN have unique behaviour specific to a J-type shock, but that such differences in behaviour are only evident at low vsand low nH. We find that CH3OH is enhanced by shocks and is a reliable probe of the pre-shock gas density. However, we find no difference between its gas-phase abundance in C-type and J-type shocks. Finally, from our application to L1157, we find that the fractional abundances within the B2 region are consistent with both C-type and J-type shock emission.

Key words. astrochemistry – evolution – ISM: individual objects: L1157 – ISM: molecules – stars: protostars

1. Introduction

Astrophysical shocks represent prominent catalysts for chemical evolution in the interstellar medium (ISM). The low signal-speed within the ambient ISM leads to a variety of different astrophysical events driving supersonic flows that form shocks, from cloud- cloud collisions (e.g.Gidalevich 1966) to bipolar outflows ema- nating from protostellar objects (e.g.Snell et al. 1980;Shu et al.

1991;Zhang & Zheng 1997). The different ambient gas conditions that a supersonic flow can be driven into leads to the pro- duction of different shock types.Draine(1980) initially defined two shock types, C (continuous) type shock and J (jump) type shock, with subsequent computational work by Chièze et al.

(1998) and Flower et al. (2003a) defining a third, CJ (mixed) type shock.

Unlike C-type shocks, which typically arise in regions with a magnetic field and low degree of fractional-ionisation, J-type shocks arise in regions whereby only a negligible magnetic field is present (Draine 1980). The negligible magnetic field within a J-type shock has further consequences in that it does not act to limit the compression through the shock, thus allowing a higher peak temperature to be reached within the shock-front (relative to a C-type shock). Owing to this, J-type shocks are thought to exhibit far more destructive chemistry than a C-type shock counterpart. An analytic description of a C-type shock therefore requires equations of magnetohydrodynamics (MHD) and mul- tiple fluid components, whilst J-type shocks can be described by hydrodynamics equations and a single fluid alone.

Typically, such descriptions are implemented in MHD codes such as mhd_vode (Flower & Des ForÉts 2015). How- ever, such approaches to modelling incur a large amount of computational expense, necessitating compromises in the complexity and size of the chemical network used. By using a parameterised form of the physical structure of the shock, as Jiménez-Serra et al. (2008) did with their C-type shock parameterisation, it is possible to preserve an approximation of the shock structure whilst significantly reducing computational complexity, thus allowing the computation of far more complex chemistry.

This is particularly important owing to the complex chemistry that is influenced by shocks. In particular, shocks can drive chemical reactions that would otherwise be highly unlikely to occur under quiescent ISM conditions. For example, the reaction O+ H2−→ OH+ H has an activation barrier of ≈1 eV and would therefore require temperatures >1000 K, which are eas- ily achievable within shocks, to initiate (Baulch et al. 1992;van Dishoeck et al. 2013;Williams & Viti 2013).

It is through such reactions that the axiom of unique chemistry as a diagnostic of prior physical events is drawn. Further reinforcing this axiom is interstellar chemistry’s high density and temperature dependence, thus rendering the composition of the ISM highly sensitive to dynamical environmental effects.

Shocks are ubiquitous sources of such change within the ISM, and therefore represent prominent sources of chemical enrich- ment in early star-forming environments.

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Observations of shocked regions allow effective probes of the shock chemistry. Recent high-resolution spectroscopy programmes such as ASAI (Lefloch et al. 2018), CHESS (Lefloch et al. 2010), and WISH (van Dishoeck et al. 2010) permit unprecedented insight into not just early stages of star formation, but also the violent events that initially drive shocks into these regions. The bipolar outflow in L1157 (Umemoto et al. 1992) is an example of a prototypical protostellar outflow observed during these programmes. Observations of outflows cannot, however, provide insight into either the physical or subsequent chemical evolution of the shock through time, instead only capturing a static snapshot of the conditions. Modelling shock-induced chemistry is therefore one of the only methods of following the evolution of an inherently time-dependent chemical process in astrophysics.

The role that dust grains play in interstellar chemistry is also of paramount importance. Molecules in the gas-phase may freeze on to the surface of dust grains, thereby depleting their gas-phase abundance by changing state. Processes such as suc- cessive hydrogenation on dust grains are thought to be the mechanism responsible for such complex organic molecule formation as CH3OH (Tielens & Whittet 1997;Fuchs et al. 2009). Impor- tantly this method also presents a viable solution to the cold gas- phase abundance problem whereby molecules are observed in the gas phase at temperatures well below their gas-phase formation temperature. Under the influence of a sputtering, grain- grain collision or desorption event (thermal or non-thermal), the molecule may be released from the surface of the dust-grain directly into the gas phase. This complex interplay between the gas-phase and dust-grain chemistry essentially chemically cou- ples the two phases. It is therefore vitally important when modelling interstellar chemistry that both gas-phase and dust-grain reactions included within the reaction network are accurate and comprehensive for the relevant molecules.

In practice, the only way one can hope to distinguish between the two types of shock is to systematically determine the effects of each shock type and hence compare the resultant chemical distinctions. Our goal in this paper is to identify molecular tracers of a J-type shock by using such a technique and apply it to a shocked region of L1157 thought to be exhibiting signatures of both C-type and J-type shock behaviour. We therefore make extensive use of the C-type shock module, based on Jiménez- Serra et al. (2008), that is already implemented in UCLCHEM (Holdship et al. 2017). To that goal, we present in Sect. 2 an overview of L1157. We present in Sect.3a parameterised model of a J-type shock built for the astrochemical code UCLCHEM.

In conjunction with the pre-existing C-type shock model based upon Jiménez-Serra et al.(2008) we investigate in Sect. 4 the chemical distinctions between J-type and C-type shocks to identify unique chemical tracers of both shock types. Section 5 applies these results by comparing them to enhanced abundances with shocked regions of the L1157 outflow.

2. L1157

At 250 pc (Looney et al. 2007), L1157 is a nearby region that comprises a central class-0 protostar, L1157-mm, that in turn drives a bipolar outflow. The observed outflow produces a red- shifted lobe to the North and a blue-shifted lobe to the South that are aligned with the protostar’s rotation axis. A degree of sym- metry is observed in these lobes, however the geometry of lobe sub-structure indicates the presence of an underlying precessing jet (Vasta et al. 2012). This precession allows periodic ejection events to create complex structures enhanced by shocks (Gueth

Fig. 1.Spitzer/IRAC 8 µm image of the L1157 outflow. (Podio et al.

2016). Shown as black squares are the shock events B0, B1 and B2. The class-0 protostar L1157-mm that drives the outflow is also labelled. The black line overplotted is the precession model thought to be responsible for the creation of the observed knots. As is visible here, B2 is far less intense in emission than B0/B1.

et al. 1996). The Southern lobe hosts two intriguing examples of such shock events: the clumps B1 and B2, which are themselves located within larger cavities C1 and C2. As a result, L1157 is considered to be one of the best laboratories for astrochemistry (Umemoto et al. 1992;Bachiller et al. 2001).

Figure1shows Spitzer/IRAC8 µmobservationsbyPodio et al.

(2016). Labelled are the knots B0, B1 and B2 alongside the central driving protostar L1157-mm and the proposed precession model fromPodio et al.(2016).

It has since been found that B1 and B2 themselves host low-velocity clumps.Benedettini et al.(2007), using PdB inter- ferometric observations, showed that nine clumps exist within the B1 and B2 structure, thus giving rise to even further complexity within the Southern lobe. This substructure is thought to arise from L1157-mm’s precession, which creates complex knots driven by shock-activity produced by the host outflow.

2.1. L1157-B1

B1 is the brightest clump within the L1157 region and thus the subject of significant study. It is warm and young, exhibiting kinetic temperatures between T ≈ 80−100 K and age t ≈ 1000 years. In comparison B2 is colder and older with T ≈ 20−60 K and t ≈ 4000 years (Tafalla & Bachiller 1995;Gueth et al. 1996). Viti et al.(2011) first showed, with confirmation by Benedettini et al. (2012), that B1 is likely produced by a non-dissociative, C-type shock with pre-shock density n_H ≥ 10⁴cm⁻³and vs ≈ 40 km s⁻¹, leading to a maximum obtainable temperature of ∼4000 K.

2.2. L1157-B2

Being less intense in most emission lines, B2 has been subject to far less study. B2 is, however, brighter than B1 in most sulphur- bearing species as well as HNCO (Tafalla & Bachiller 1995;

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Table 1. Abundances χ of known shock enhanced molecules and their enhancement factors f (relative to χ(0)) in the two L1157 knots B1 and B2.

Molecule χ(0) χ(B1) χ(B2) f(B1) f(B2) Reference

CH3OH 4.5 × 10⁻⁸ 0.4−1.9 × 10⁻⁵ 2.2 × 10⁻⁵ 300−400 500 (1)

HCN 3.6 × 10⁻⁹ 3.3 × 10⁻⁷ 5.5 × 10⁻⁷ 90 150 (1)

SO ∼5.0 × 10⁻⁹ 2.0−3.0 × 10⁻⁷ 2.0−5.0 × 10⁻⁷ 50−70 60−100 (1)

SO2 /3.0 × 10⁻⁸ 2.1 × 10⁻⁷ 5.7 × 10⁻⁷ ∼8 ∼20 (1)

H₂O (. . . ) 1 × 10⁻⁴ 1 × 10⁻⁶ (. . . ) (. . . ) (2)

HNCO 0.3−1.2 × 10⁻⁹ 4.3−17.9 × 10⁻⁹ 25−96 × 10⁻⁹ ∼15 ∼80 (3) Notes.χ(0) is the fractional abundance of each molecule measured towards the central driving protostar L1157-mm.

References. (1)Bachiller & Pérez Gutiérrez(1997); (2)Vasta et al.(2012); (3)Rodríguez-Fernández et al.(2010).

Bachiller & Pérez Gutiérrez 1997;Rodríguez-Fernández et al.

2010).Tafalla & Bachiller(1995) specifically finds that SO and SO2 exhibit enhancement factors within L1157-B2 (relative to L1157-mm) of between 60−100 and 20, respectively. Mean- while, they also find that the enhancement factors for L1157-B1 are 50−70 and 8. HNCO is thought to form efficiently on grain surfaces, whilst S-bearing species like SO and SO2 form in the gas-phase with sputtered S from the grains themselves (Allen &

Robinson 1977;Charnley 1997;Garrod et al. 2008). The older dynamical age of B2 relative to B1 could lend credence to the idea that B2 has simply had more time than B1 to chemically process the sputtered material, hence the more luminous species like HNCO and S-bearing species. Table1lists further molecules observed within L1157 and their enhancement factors, where fenhance = χ(R)/χ(0). Importantly these enhancement factors, as well as their associated abundances, are subject to large uncertainties arising from the assumption that the observed lines are both optically thin and thermalised.

To date studies such as those byVasta et al.(2012) have not yet been able to determine with certainty the prevalent shock type within B2, thoughVasta et al.(2012) does allude to the pos- sibility of a J-type shock component within L1157-B2.Gómez- Ruiz et al. (2016) use NH3 and H2O abundances, alongside model predictions, to trace shock temperature within L1157’s lobes. Gómez-Ruiz et al.(2016) finds that whilst a proper line radiative transfer model is needed for proper computation, the best matching model for L1157-B2 is one with n_H ≈ 10³cm⁻³ and vs≈ 10 km s⁻¹.

3. Shock modelling

Our parameterised model is based on the MHD code mhd_vode (Flower & Des ForÉts 2015). mhd_vode is an ideal-MHD, 1D, two-fluid simulation of both C-type and J-type shocks that com- putes chemistry in parallel with its physics. This model is built as a module to the time-dependent chemical code UCLCHEM (Holdship et al. 2017).

UCLCHEM is a diverse code, and its modularised functionality lends itself to a host of different astrochemical problems and environments. For a full description of UCLCHEM’s operation see Holdship et al. (2017) as well as the documentation hosted online¹. In brief, UCLCHEM is constructed so as to follow a two-phase computation. Firstly an ambient medium of user-supplied temperature, density and chemical composition undergoes an isothermal collapse as described byRawlings et al. (1992) to a user-supplied final density. The chemical composition of a 1D parcel is therefore followed during collapse, and thus informs the chemical conditions for phase 2.

During phase 2, the relevant physics supplied via a user module

1 https://uclchem.github.io/

is computed and used to inform the rates of reactions within the chemical network. Our J-type shock module is built so as to follow this methodology.

3.1. J-type shock parameterisation

To construct our parameterised model we first noted that, as described byZel’dovich & Raizer(1967), shocks can generally be discretised into four regions: the precursor, the shock-front, the post-shock relaxation layer and the thermalisation layer. We neglect the radiative precursor component of the shock in our models, as J-type shocks with v_s< 80 km s⁻¹have been found to have negligible radiative precursor components, therefore play- ing no role in either the shock structure or the shock chemistry (Hollenbach & McKee 1989; Flower et al. 2003b). We also neglect the thermalisation layer, instead focusing on the shock-front and the post-shock relaxation layer as sole sources of chemical evolution. We assume that the post-shock gas cools to its initial temperature in the post-shock relaxation layer.

To build the shock-front, we ran a grid of mhd_vode models with the magnetic field B = 0 G and interstellar values for cosmic-ray ionisation rate ζCR and radiation field, so as to quantify the trend in temperature and density, as well as the shock-front duration tfront, across the parameter space we were exploring. tfront, in units of s, is described by Eq. (1).

tfront=

√ 2π

5.76 × 10⁻¹⁶−1

v_s× 10⁶ (1)

where vs represents the initial shock velocity in km s⁻¹. The increase in temperature and density within the shock-front was found to be best described by T = Tmax(t/tfront)² in K and nH = 4nH_initial(t/tfront)⁴ in cm⁻³. For t < tfront we assume that the Rankine-Hugoniot conditions (Rankine 1870; Hugoniot 1889) hold such that the density nH increases to ≈4 times its initial value whilst the temperature T increases to its maximum obtainable value, Tmax. Tmaxis determined by Tmax = 5 × 10³(vs/10)² in K (Williams & Viti 2013).

After the shock-front, the shocked gas begins to cool, rep- resenting the post-shock relaxation layer where t > tfront and t < t_shock. tshock was obtained by fitting a polynomial to a range of shock timescales from mhd_vode models and is described by Eq. (2).

t_shock= tyear× 10⁶ nHinitial

(2) where t_year is the number of seconds in 1 year and n_H_initial is the initial pre-shock number density in cm⁻³. The factor of 10⁶acts as a normalising density such that t_shockhas units of s.

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Within this layer, the temperature and density equations take the forms described in Eqs. (3) and (4).

T = Tmaxe^−λ^T

t tshock

(3) n= 4ninitiale^λⁿ

t tshock

. (4)

Equation (3) has units of K, whilst Eq. (4) has units of cm⁻³. This therefore allows the gas to cool following a decaying expo- nential law, whilst the gas also increases in density to nH_max, which is itself derived from mhd_vode grids. n_H_max is defined as nH_max= (vs× nH_initial) × 10²in units of cm⁻³. The constants λT

and λn in Eqs. (3) and (4) are described by λT = ln(_T^T_initial^max) and λ_n = ln(_nⁿ_initial^max). At t > t_shock, we assume that the gas has cooled back to its initial temperature Tinitial. We assume a steady-state profile for both T and n, and discuss the validity of this approximation in Sect.4.1.

3.2. C-type shock parameterisation

UCLCHEM implements a version of the parameterised C-type shock fromJiménez-Serra et al.(2008). The UCLCHEM implementation is described in more detail, as well as demonstrated to good effect, inHoldship et al.(2017).

Similarly to the J-type shock parameterisation presented in Sect. 3,Jiménez-Serra et al.(2008) approximates the physical shock structure using analytical equations for T and n_Halong- side the velocity of the ions and neutrals, viand vnrespectively (see Appendix A ofJiménez-Serra et al. 2008for further details).

They also make use of results fromDraine et al.(1983) to param- eterise the maximum shock temperature Tmax as a function of shock velocity v_s. It is this temperature that is shown for the C-type shock in Table2.

Jiménez-Serra et al.(2008) also present, in Appendix B, a fractional sputtering treatment of grain mantle species such Si, CH3OH, and H2O. UCLCHEM now supports this sputtering implementation. In summary, rather than an instantaneous ejection of the mantle into the gas phase when the saturation time tsat2is exceeded, only a fraction of the species abundance will be released from the mantles and/or ices at any given timestep providing the drift velocity between the neutrals and ions, as well as the impact energy, is sufficient to sputter material.

Of critical importance in C-type shock formation is the magnetic field, B. UCLCHEM’s C-type shock implementation assumes the B-field (in µG) scales according to the emperical law defined inDraine et al.(1983), i.e. B0 = b0

√nHwhere b0

is the magnetic scaling parameter and nHthe Hydrogen number density. Much likeDraine et al.(1983), we fix b₀as 1, thus allowing the magnetic field to scale with √

nHas defined in Table 4 of Draine et al.(1983). According to this relation, at nH= 10³cm⁻³ the magnetic field has a field strength of B0 = 10 µG whilst at nH= 10⁶cm⁻³the magnetic field has field strength B0 = 1 mG, both of which are consistent with Table 4 ofDraine et al.(1983).

3.3. Computational grid

Gómez-Ruiz et al. (2016) finds the best fit profile to NH3 and H2O abundances in L1157-B2 is one with vs = 10 km s⁻¹and nH= 10³cm⁻³, and we use this as to inform our choice of initial conditions for our grid of models.

2 tsat is defined as the time for which the logarithmic difference of the Si abundance between two consecutive timesteps ti+1 and ti is

log10χ(mi+1) − log₁₀χ(mi) < 0.1.

Table 2. Grid of models used to compute simulations.

Model nH[cm⁻³] vs[km s⁻¹] Tmax[K]

C-type J-type

1 10³ 5 85 1250

2 10⁴ 5 85 1250

3 10⁵ 5 85 1250

4 10⁶ 5 85 1250

5 10³ 6 131 1800

6 10⁴ 6 131 1800

7 10⁵ 6 131 1800

8 10⁶ 6 131 1800

9 10³ 7 178 2450

10 10⁴ 7 178 2450

11 10⁵ 7 178 2450

12 10⁶ 7 178 2450

13 10³ 8 225 3200

14 10⁴ 8 225 3200

15 10⁵ 8 225 3200

16 10⁶ 8 225 3200

17 10³ 9 273 4050

18 10⁴ 9 273 4050

19 10⁵ 9 273 4050

20 10⁶ 9 273 4050

21 10³ 10 323 5000

22 10⁴ 10 323 5000

23 10⁵ 10 323 5000

24 10⁶ 10 323 5000

25 10³ 11 373 6050

26 10⁴ 11 373 6050

27 10⁵ 11 373 6050

28 10⁶ 11 373 6050

29 10³ 12 424 7200

30 10⁴ 12 424 7200

31 10⁵ 12 424 7200

32 10⁶ 12 424 7200

33 10³ 13 477 8450

34 10⁴ 13 477 8450

35 10⁵ 13 477 8450

36 10⁶ 13 477 8450

37 10³ 14 530 9800

38 10⁴ 14 530 9800

39 10⁵ 14 530 9800

40 10⁶ 14 530 9800

41 10³ 15 585 11 250

42 10⁴ 15 585 11 250

43 10⁵ 15 585 11 250

44 10⁶ 15 585 11 250

Notes. The velocity vs, density nHand maximum temperature achieved in both C-type and J-type shocks, Tmax, is shown. Each model is run twice: once for a C-type shock and once for a J-type shock.

Table 2 shows the range of parameters used to compute this grid. For a J-type shock Tmax is determined as discussed, whilst for a C-type shock Tmax is determined according to the parameterisation discussed inJiménez-Serra et al. (2008) (see Sect.3.2).

We also account for the initial C-type shock conditions published by other authors so as to verify the feasibility of C-type

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10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ d (cm)

10¹ 10² 10³

T(K)

mhd vode UCLCHEM

Fig. 2.Comparing the temperature structure of a J-type shock with v= 10 km s⁻¹and nH= 10³cm⁻³computed with the model presented in this paper and the mhd_vode model byFlower & Des ForÉts(2015). Good agreement is observed, despite our approximation not recovering all of the features in the mhd_vode profile. The model built for UCLCHEM is also isothermal such that it cools back to its initial temperature, whereas mhd_vode is not despite it cooling to ≈10 K in this instance.

shock formation at the conditions considered. For example Holdship et al.(2017) identifies C-type shock-tracing molecules for a range of different physical shock conditions to a lower limit of v_s= 10 km s⁻¹and n_H= 10³cm⁻³. Furthermore,Draine et al.

(1983) identify the maximum shock temperature for a range of different C-type shocks with a lower limit of vs = 5 km s⁻¹and nH = 10²cm⁻³ with a B field defined by B = 10 µG. Finally, Godard et al.(2019) investigate the formation of a range of different shock types under different B fields and irradiated conditions. They highlight C-type shocks forming between vs = 5−20 km s⁻¹and n_H = 10²−10⁵cm⁻³ under a range of B fields from B= 1 µG to B = 3 mG. Our parameters fit comfortably into this published range and we therefore assume that C-type shock formation at these conditions is entirely feasible.

For each vsand nHwithin Table2, the fractional abundance of 215 individual molecules, including H2O, HCN, CH3OH, SO and SO2, was computed for both C-type and J-type shocks. This was achieved by coupling the physical shock computations from within the physics modules of UCLCHEM to a chemical network of 2456 reactions. Further details of the network are discussed later in this section. We plot the fractional abundance of a molecule against distance through the shock, up to the C-type shock dissipation length as determined byJiménez-Serra et al.

(2008). The dissipation length is defined as the distance over which the velocity of the ions and neutrals equalises (Draine 1980). As a J-type shock consists of one fluid that encompasses both ions and neutrals, the concept of a dissipation length does not apply. Instead, we plot the J-type shock fractional abundance up to the cooling length of the shock, beyond which the gas has reached equilibrium. As the fluids within a C-type shock also reach equilibrium at the dissipation length, we assume the two distance scales are comparable.

Using these plots, the abundance trends were then com- pared between shock types to better understand the behaviour of species under different shock conditions. Of particular interest in this study was the enhancement factors observed in Table1, as this forms the signature of shock passage and therefore the best diagnostic of shock type in a shocked region.

10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ d (cm)

10³ 10⁴ 10⁵ 10⁶

nH(cm−3)

mhd vode UCLCHEM

Fig. 3. Like Fig. 2, here we compare the density profiles for the J-type shock in mhd_vode, as well as the model presented in this paper.

Good agreement is again observed, despite the lack of inflexion point recovery.

Principal to this enhancement factor analysis is the assumption that the pre-shock gas is homogeneous throughout L1157 and the surrounding region, therefore allowing the fractional abundance at t ≈ 0 years in phase 2 to be consistent with non- shocked regions of gas outside the shocked knots. This may only be true for the B2 region, as previous work (Viti et al. 2011) has indicated that a pre-existing, non-homogeneous clump is required for the extant chemistry at B1 to occur. To date, there is no such evidence observed towards B2, hence the homogeneous pre-shock gas assumption. Using this, we can also compute enhancement factors relative to the fractional abundance at t ≈0 years, thus allowing direct comparison to the abundances and enhancement factors listed in Table1.

The chemical network used to compute the abundances considered is based on the network described by Holdship et al.

(2017). To summarise in brief, we use a reduced form of the UMIST database (McElroy et al. 2013) to build a network of gas- phase reactions. We also include a dust-grain reaction network that allows for freeze out with hydrogenation and both thermal and non-thermal desorption.

4. Results

4.1. Model comparison

Figure2shows the profile of temperature T , whilst Fig.3shows the profile of density nHfor both mhd_vode and the model presented in this work.

Qualitatively comparing the T profiles in Fig. 2 we observe good agreement between the mhd_vode model and the UCLCHEM model’s computation of T in the shock-front described by Eq. (3). Both models reach approximately the same T_max over an almost identical distance despite the UCLCHEM model beginning its heating prior to the mhd_vode model.

Further agreement is observed until d ≈ 10¹¹cm, whereby mhd_vode begins to cool rapidly, further exhibiting an inflexion point at d ≈ 10¹³cm, causing T to drop from 5000 K to 300 K.

As a result agreement diverges between 10¹¹ < d < 10¹⁴cm.

This departure is a consequence of mhd_vode’s radiative cooling, which UCLCHEM does not implement.

Furthermore mhd_vode does not explicitly cool back to its initial temperature, though it does reach an equilibrium

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10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ d (cm)

10⁻⁹ 10⁻⁸ 10⁻⁷ 10⁻⁶ 10⁻⁵ 10⁻⁴

χSpecies

Flower: H2O UCLCHEM: H2O

Fig. 4.Evolution of H2O during the shock referenced in Figs.2and3 in both mhd_vode and UCLCHEM. Within this figure, sputtering has been deactivated in UCLCHEM for the purposes of comparison. This implies that only gas-phase chemical reactions are active in these simulations so that the effect of the differences in the temperature profiles between mhd_vode and our approximation can be fairly evaluated. The abundance evolution of H2O up to d ≈ 10¹³cm is in almost perfect agreement. This is in spite of the lack of inflexion point in both T and n between 10¹¹< d < 10¹⁴cm. This proves that such a departure has negligible effect during the shock. mhd_vode manually cools H2O, hence the decrease in abundance at d ≈ 10¹⁴cm. UCLCHEM does not implement this cooling.

temperature very close to that of its initial temperature. Figure2 shows the mhd_vode model cooling its gas to ≈10 K after d ≈ 10¹⁴cm. The parameterised model presented here explicitly assumes that the gas cools back to Tinitial. In Fig.2 this is 10 K.

Comparisons between nHmodels in Fig.3show qualitatively less agreement, especially regarding the peak nH. However, the UCLCHEM peak n_H is within a factor of 2 of the mhd_vode model.

The inflexion point highlighted in Fig. 2 is also present within Fig. 3at the same time. Similarly to before, we do not attempt to recover this feature. To assess the effect that this miss- ing feature has on our approximation, and the subsequent chemistry that this model is used to inform, we directly compare the chemistry of H₂O between mhd_vode and UCLCHEM. This is seen in Fig.4. Importantly, the public version of mhd_vode used in this study does not include sputtering. Therefore for this comparison, we disable UCLCHEM’s sputtering treatment to compare chemistry with the same major gas-grain treatments present.

For the same initial conditions, mhd_vode and UCLCHEM produce the same H2O abundance behaviour despite UCLCHEM not recovering the observed inflexion point.

This is true up to d = 10¹⁴cm, where mhd_vode radiatively cools H₂O, causing its abundance to drop sharply. UCLCHEM does not implement this form of cooling and so the H2O abundance does not drop sharply until a much greater distance into the shock.

Given that our model is never more than a factor of 3 away from the mhd_vode equivalent, and that the shocked H2O abundances are in almost perfect agreement, we consider our parameterisation of a J-type shock a good approximation of an equivalent shock model from an ideal-MHD simulation such as mhd_vode.

Part of our model is the simplifying assumption that the shock is steady-state. This is valid and physically justified as

long as the cooling time of the shock is shorter than the time for which the shock velocity and the pre-shock conditions of the gas can change (Martinez 2009). In our grid runs, we switch back on grain chemistry and assume that the mantle ices instantaneously evaporate if the temperature of the gas T > 100 K.

This is derived from plots withinFraser et al.(2001). We also assume that any species that have formed in the solid-state on the dust-grain will co-desorb alongside the mantle ices.

We note that the instantaneous evaporation of the ices in J-type shocks occurs before sputtering takes place. This is fully justified since this is the expected behaviour from the J-type shock’s rapid heating of gas and dust at the sharp shock front.

For C-type shocks, we consider both processes, ice evaporation when T exceeds 100 K and sputtering. Since T is significantly lower in C-type shocks, evaporation is less efficient and so sputtering is more effective at releasing a fractional amount of the ices into the gas phase (see Jiménez-Serra et al. 2008, for details on the fractional sputtering technique implemented in UCLCHEM).

The qualitative agreement noted thus far between mhd_vode model and our parameterised model validates our steady-state assumption for the initial shock conditions applied here.

4.2. Identifying J-type shock behaviour

To identify unique J-type shock behaviour, we determine the average abundance across the post-shock region³ arising as a result of both J-type and C-type shocks for each model within our grid, and express the ratio of these two average abundances, χ(J)/χ(C). J-type shock enhanced molecules are therefore molecules that have χ(J)/χ(C) 1.

To assess the distribution of ratios across the entire grid we bin each model by its values of vs and nHand construct a 2D colour plot. The colour within each bin represents the ratio of the average post-shock abundances, χ(J)/χ(C), up to the dissipation length (or equivalent) for both shock types.

We also use the enhancement factor, fenhance, as a diagnostic.

We define fenhancein Eq. (5).

fenhance =χ(R)

χ(0) (5)

χ(R) is the fractional abundance of the shocked molecule, whilst χ(0) is the fractional abundance of the molecule in a quiescent state. Within this study, we take χ(0) to be the abundance at simulation time t ≈ 0 years before any sputtering takes place. f_enhance is therefore directly comparable to f in Table1.

This analysis was performed for a range of different known shock-tracing molecules including CH3OH, H2O, SO, SO2and HCN. We also investigated the behaviour of molecules such as SiO, however our analysis indicated that its behaviour was not noteworthy at the considered conditions. We attribute this to our shock velocities v_sbeing too slow to efficiently sputter and form SiO.

4.2.1. CH3OH

Figure5shows the ratio of the average post-shock abundances up to the dissipation length (or equivalent) for each shock type.

It is computed for C-type shock and J-type shock enhanced

3 For the J-type shocks we define the post-shock region as that found between the shock-front and the end of the cooling region; while for a C-type shock, the post-shock region coincides with the length of the dissipation region of the shock.

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5 6 7 8 9 10 11 12 13 14 15 vs (km s⁻¹)

10³ 10⁴ 10⁵ 10⁶

nH(cm−3)

10⁰ 10¹ 10² 10³

χ(J)/χ(C)

Fig. 5. Ratio of the average J-type enhanced CH3OH abundance to the average C-type enhanced CH3OH abundance. As is clear, there is no chemical difference between J-type and C-type enhanced CH3OH, except at low vsand low nH. This major difference – a factor of 8000 – arises as a result of the C-type shock failing to sputter grain surface material whilst the J-type shock instantaneously evaporates grain surface CH3OH.

10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ d (cm)

10⁻¹⁵ 10⁻¹³ 10⁻¹¹ 10⁻⁹ 10⁻⁷

χSpecies

C-shock: CH3OH J-shock: CH3OH

Fig. 6. CH3OH abundances for a shock with initial velocity vs = 5 km s⁻¹and density nH = 10³cm⁻³. The shaded red region indicates the region beyond which the J-type shock has cooled to its equilibrium temperature.

CH3OH for each model in the grid described in Table2. Within this figure, χ(C) represents the average gas-phase abundance in a C-type shock achieved up to the dissipation length, whilst χ(J) is the average gas-phase abundance up to the cooling length for a J-type shock.

Figure 5 shows that there is essentially no difference in chemistry between shock type for CH3OH, except the models where vs = 5 km s⁻¹ and nH = 10³cm⁻³ as well as nH = 10⁴cm⁻³.

This unique disparity stems from the stark difference in gas- grain behaviour between shock types under these conditions. As Fig.6shows, the CH3OH abundance sharply increases as a result of instantaneous evaporation at d ≈ 10⁷cm in the J-type shock.

In the C-type shock, neither evaporation nor sputtering occurs, meaning the CH3OH abundance remains relatively consistent throughout the shock.

This is confirmed in Figs.6and7, which shows the CH3OH abundance as a function of distance through both C-type and J-type shocks with velocity vs = 5 km s⁻¹ and density nH = 10³cm⁻³and n_H= 10⁶cm⁻³.

At conditions excluding those already discussed, sputtering becomes efficient, hence the abundance ratios in Fig.5tending to

10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ d (cm)

10⁻¹⁵ 10⁻¹³ 10⁻¹¹ 10⁻⁹ 10⁻⁷ 10⁻⁵

χSpecies

C-shock: CH3OH J-shock: CH3OH

Fig. 7. CH3OH abundances for a shock with initial velocity vs = 5 km s⁻¹and density nH= 10⁶cm⁻³. Again, the shaded red region indicates the region beyond which the J-type shock has cooled to its equilibrium temperature.

5 6 7 8 9 10 11 12 13 14 15

vs(km s⁻¹) 10³

10⁴ 10⁵ 10⁶

nH(cm−3)

10⁰ 10¹ 10² 10³

χ(J)/χ(C)

Fig. 8.Ratio of the average J-type enhanced H2O abundance to the average C-type enhanced H₂O abundance. The largest difference between average shock type abundance is at vs = 5 km s⁻¹and nH = 10³cm⁻³ and nH= 10⁴cm⁻³where the ratio exceeds 1000.

1 uniformly throughout the rest of the grid as a result of CH3OH being co-desorbed in a J-type shock and sputtered in a C-type shock in equal measure. Importantly, following injection/sputtering there is minimal subsequent gas-phase chemistry in either shock, hence reinforcing the common abundances achieved in Fig.5regardless of shock type.

As a result of the J-type shock’s rapid heating, instantaneous evaporation occurs well before any sputtering activity in a C-type shock. In both shocks, the same amount of CH₃OH is released from the dust-grains owing to self-consistent initial conditions from phase 1 of UCLCHEM.

4.2.2. H₂O

The abundance ratios for H₂O is shown in Fig. 8. Much like CH3OH in Sect.4.2.1, H2O behaves similarly at vs = 5 km s⁻¹ and nH= 10³cm⁻³as well as nH= 10⁴cm⁻³owing to the same processes; in other words the J-type shock instantaneously evaporates material whilst the C-type shock neither sputters nor evaporates.

Outside of this, the biggest difference between C-type and J-type shocks peaks at v_s < 10 km s⁻¹and n_H = 10³cm⁻³. The enhancement factors drop off to ≈1 at velocities and densities greater than these.

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10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ d (cm)

10⁻⁷ 10⁻⁶ 10⁻⁵ 10⁻⁴

χSpecies

C-shock: H2O J-shock: H2O

Fig. 9.H2O abundances for a shock with initial velocity vs = 5 km s⁻¹ and density nH= 10³cm⁻³.

10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ d (cm)

10⁻⁹ 10⁻⁸ 10⁻⁷ 10⁻⁶ 10⁻⁵ 10⁻⁴

χSpecies

C-shock: H2O J-shock: H2O

Fig. 10.H2O abundances for a shock with initial velocity vs= 5 km s⁻¹ and density nH= 10⁶cm⁻³.

Figures9and10shows the H2O abundances as a function of distance through the shock for C-type and J-type shocks with velocity v_s= 5 km s⁻¹and density n_H= 10³and n_H= 10⁶cm⁻³. In the J-type shock profiles from Figs. 9 and 10, the gas phase abundance of H₂O increases sharply at ≈10⁷cm. This feature arises as a result of evaporation of the solid state material frozen on to the dust grains, e.g. the ices. The C-type shock may also undergo an increase in gas phase H2O at a later time in the shock as a result of sputtering, providing that the initial shock conditions enable the sputtering process. In our models, sputtering does not occur at vs= 5 km s⁻¹and nH= 10³cm⁻³as well as nH= 10⁴cm⁻³, hence the large difference in average abundance at these models in Fig.8.

Post-evaporation features within Figs. 9 and 10 begin to explain the more minor gas-phase enhancement in Fig. 8. For the J-type shock in Fig. 9, the abundance of H2O increases to a maximum of ≈3 × 10⁻⁴, approximately 6 times the post- evaporation abundance, at around d ≈ 10¹³ cm. This effect is largest at nH= 10³cm⁻³and is present as nHincreases, though the magnitude of the gas-phase enhancement does decrease as n_H increases. At n_H = 10⁶cm⁻³ (Fig. 10) there is no post- evaporation gas phase abundance change in H2O, thus eliminat- ing the effect altogether.

5 6 7 8 9 10 11 12 13 14 15

vs(km s⁻¹) 10³

10⁴ 10⁵ 10⁶

nH(cm−3)

10⁻² 10⁻¹ 10⁰ 10¹

χ(J)/χ(C)

Fig. 11.Ratio of the average J-type enhanced SO abundance to the average C-type enhanced SO abundance. The largest difference between peak shock type abundance is at nH = 10³cm⁻³. The shock conditions that produce unique chemistry in this parameter space are those with nH< 10⁵cm⁻³.

Investigating the C-type shock in Figs.9and10, we observe no post-sputtering increase in H2O, regardless of nH. This, cou- pled with the decreasing gas-phase enhancement in the J-type as nHincreases, results in both shock types tending to the same abundance.

This explains why the largest enhancement is seen at low v_s, low nH. As nHincreases, an overall decrease in the post-injection gas phase abundance change is observed, despite the evaporated H2O increasing with nH. As vs increases, the peak temperature of the shock also rises, allowing gas-phase H2O to be destroyed.

For a J-type shock, H2O destruction begins at vs = 11 km s⁻¹ when Tmax> 6000 K.

4.2.3. SO

Figure11shows the average abundance ratios for SO. Interest- ingly, Fig.11shows that SO is not produced more efficiently in a J-type shock than a C-type shock in our parameter space. In actuality, for n_H> 10⁴cm⁻³the ratio χ(J)/χ(C) ≈ 1, indicating that at high density both shocks are able to enhance SO to similar degrees.

The behaviour of SO at nH < 10⁴cm⁻³is starkly different.

Considering the n = 10³cm⁻³ row within Fig. 11, it can be observed that the peak ratio of ≈10 occurs at vs = 5 km s⁻¹. To explain such behaviour, consider the SO abundance as a function of distance in Figs.12and13for a shock of v_s= 5 km s⁻¹with density from nH= 10³cm⁻³and nH= 10⁶cm⁻³.

Comparing the v_s = 5 km s⁻¹ and n_H = 10³cm⁻³ model in Fig.11 with the abundance profile for the same initial conditions in Fig.12begins to explain the peak abundance ratio. It is clear that this arises as a result of the J-type shock injecting SO from the grain surface, whilst the C-type shock cannot sputter at these conditions. As d approaches 10¹³cm the SO abundance peaks at around 10⁻⁷ – an enhancement relative to the initial SO abundance of ≈100. However, towards d ≈ 10¹³cm the SO abundance drops off sharply as SO is destroyed. This destruction skews the average SO abundance, hence the peak abundance ratio in Fig. 11 being far smaller than the peak enhancement of 100. Moreover, Tmax of a C-type shock of vs = 5 km s⁻¹ is 85 K. Such a minimal change in T through the shock is not sufficient to drive any significant gas-phase chemistry, hence the SO abundance remaining relatively constant throughout the shock in Fig.12.

Additionally, as v_s increases the C-type shock sputtering becomes more effective whilst the J-type shock destroys SO at high T , resulting in the average post-shock abundance in a J-type

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10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ d (cm)

10⁻¹³ 10⁻¹² 10⁻¹¹ 10⁻¹⁰ 10⁻⁹ 10⁻⁸ 10⁻⁷ 10⁻⁶

χSpecies

C-shock: SO J-shock: SO

Fig. 12.SO abundances for a shock with initial velocity vs = 5 km s⁻¹ and density nH= 10³cm⁻³.

10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ d (cm)

10⁻¹¹ 10⁻¹⁰ 10⁻⁹ 10⁻⁸ 10⁻⁷ 10⁻⁶

χSpecies

C-shock: SO J-shock: SO

Fig. 13.SO abundances for a shock with initial velocity vs = 5 km s⁻¹ and density n_H= 10⁶cm⁻³.

shock being less than the equivalent C-type shock. For example at v_s = 15 km s⁻¹ and n_H = 10³cm⁻³, the J-type shock average abundance is 3 × 10⁻²times smaller than the C-type shock equivalent.

This is true of the models at nH = 10⁴cm⁻³as well, though here we note that the C-type shock sputtering is more efficient therefore exacerbating the differences between average abundance in shock type. Evident here is the J-type shock abundance at v_s= 15 km s⁻¹and n_H= 10⁴cm⁻³being 1×10⁻²times smaller than C-type shock equivalent.

Figures12and13also shows that as n_Hincreases, the abundances at large d between shock types behaves universally and tends to a similar limit indicating that the dominant destruction mechanism becomes a density limited process. This therefore means that at lower nH, the enhancement is governed by a com- bination of gas-phase and dust-grain chemistry, whilst at large values of nHthe enhancement factor is governed by dust-grain chemistry alone.

4.3. SO₂

Figure 14 shows the abundance ratios for SO₂. Evident when considering Fig. 14 is the similarity between it and the SO behaviour in Fig.11. Given that SO₂can form via SO dependent

5 6 7 8 9 10 11 12 13 14 15

vs(km s⁻¹) 10³

10⁴ 10⁵ 10⁶

nH(cm−3)

10⁻² 10⁻¹ 10⁰ 10¹ 10²

χ(J)/χ(C)

Fig. 14.Ratio of the maximum J-type enhanced SO2 abundance to the maximum C-type enhanced SO2abundance. The largest difference between peak shock type abundance is at nH= 10³cm⁻³much like the SO abundance in Fig.11.

10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ d (cm)

10⁻¹⁶ 10⁻¹⁴ 10⁻¹² 10⁻¹⁰ 10⁻⁸ 10⁻⁶

χSpecies

C-shock: SO2 J-shock: SO2

Fig. 15.SO2abundances for a shock with initial velocity vs= 5 km s⁻¹ and density of nH= 10³cm⁻³.

reactions such as O+ SO −→ SO2, the similarity in behaviour is not surprising.

Figure 14 shows largely the same trends as Fig. 11 did.

For instance, we see the same behaviour in χ(J)/χ(C) ≈ 1 at nH> 10⁴cm⁻³in Fig.11, along with the same model having the same abundance ratio in Fig.11. Curiously, this peak abundance ratio is ≈200, whilst in Fig.11it was ≈10. These global trends and behaviour are expected given the close chemical relationship between SO and SO2.

Figures15and16shows the SO2 abundances as a function of distance for both C-type and J-type shocks at v = 5 km s⁻¹ through nH = 10³cm⁻³ and nH = 10⁶cm⁻³. Much like SO in Figs.12and13, both C-type and J-type shock abundance tend to the same value as nHincreases. Furthermore the same behaviour is seen at low nH. This implies that any changes to SO in a shock should be mirrored – at least in terms of qualitative behaviour – by SO2as well.

4.4. HCN

As Fig. 17 shows, the peak abundance ratio occurs at vs <

9 km s⁻¹ and nH = 10³cm⁻³, with the degree of this ratio decreasing as vsincreases. As discussed before in Sects.4.2.1–

4.2.3and4.3, it is the stark differences in sputtering and evaporation behaviour between shock types at these conditions that gives rise to this feature.

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10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ d (cm)

10⁻¹⁰ 10⁻⁹ 10⁻⁸ 10⁻⁷ 10⁻⁶ 10⁻⁵

χSpecies

C-shock: SO2 J-shock: SO2

Fig. 16.SO2abundances for a shock with initial velocity vs = 5 km s⁻¹ and density of nH= 10⁶cm⁻³.

5 6 7 8 9 10 11 12 13 14 15

vs(km s⁻¹) 10³

10⁴ 10⁵ 10⁶

nH(cm−3)

10⁰ 10¹

χ(J)/χ(C)

Fig. 17. Ratio of the average J-type enhanced HCN abundance to the average C-type enhanced HCN abundance. The largest difference between peak shock type abundance is at vs < 9 km s⁻¹ and nH = 10³cm⁻³. High vs, low nH shocks show C-type shocks are more efficient enhancers of HCN than equivalent J-type shocks.

Much like SO and SO₂ beforehand, the ratio for n_H >

10⁴cm⁻³ of Fig. 17 shows very little departure from 1 indicating that both shock types enhance HCN to the same or similar degree. Again similarly to SO and SO2 the enhance- ments at vs = 12−15 km s⁻¹and nH = 10³−10⁴cm⁻³ indicate C-type shocks are more effective enhancers of HCN than a J-type shock. As Table2 shows, J-type shocks have far higher T_maxthan an equivalent C-type shock. This implies that between vs= 12−15 km s⁻¹J-type shocks are capable of destroying HCN whilst an equivalent C-type shock cannot reach a similarly high T, therefore allowing HCN to continue formation or not undergo destruction at all.

Individual abundance profiles for HCN are shown in Figs.18 and 19. As is consistent with other figures, the immediate post-evaporation abundance increases as n_H. Despite this, the maximal post-shock gas-phase enhancement of HCN is at lower density, with the effect dropping off as nHincreases.

Much like previous figures, Fig.18explains why the J-type shock HCN abundance is so much greater than the C-type shock HCN abundance. Similarly to before, C-type shock sputtering is not possible at vs = 5 km s⁻¹ and nH = 10³cm⁻³ whilst the J-type shock is capable of instantaneously evaporating the grain-mantle material. Unlike previous molecules however, this behaviour continues up to v_s = 12 km s⁻¹. As n_H increases to nH = 10⁶cm⁻³sputtering becomes more efficient and the post- evaporation abundance increases no longer occur. Both of these

10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ d (cm)

10⁻¹¹ 10⁻¹⁰ 10⁻⁹ 10⁻⁸ 10⁻⁷ 10⁻⁶ 10⁻⁵

χSpecies

C-shock: HCN J-shock: HCN

Fig. 18.HCN abundances for a shock with initial velocity vs= 5 km s⁻¹ and density of nH= 10³cm⁻³.

10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ d (cm)

10⁻¹⁰ 10⁻⁹ 10⁻⁸ 10⁻⁷

χSpecies

C-shock: HCN J-shock: HCN

Fig. 19.HCN abundances for a shock with initial velocity vs= 5 km s⁻¹ and density of nH= 10⁶cm⁻³.

factors combined allows the HCN abundance in both shock types to tend to the same limit of ≈5 × 10⁻⁸. As shown by Fig. 17, this behaviour occurs at all values of v_s for n_H = 10⁵cm⁻³and nH= 10⁶cm⁻³.

5. The shocks in L1157-B2

Vasta et al.(2012) observed H₂O lines towards the B1 and B2 knots of L1157. In conjunction with theoretical shock models, they theorise that J-type shocks could be a prominent source of this emission. Consequently, having thus far found sev- eral unique J-type shock chemical distinctions, specifically with respect to H₂O and HCN, we qualitatively apply the results from our grid of models to the B2 region of L1157 in an effort to further categorise the type of shock responsible for its emission.

We also compare the results to the measured abundances and enhancement factors in Table 1 to further constrain the shock type. Crucially, as mentioned in Sect.2.2, the measured abundances are likely subject to large uncertainties owing to the optically thin and thermalised line assumptions required to determine them.

We focus on B2 and not B1 for a number of reasons. Firstly, Gusdorf et al.(2008) theorised that B1 is the result of a combi- nation of C-type and J-type shocks, especially in regards to the